Various types of flexible roll-up truck covers employing tarpaulins and the like have heretofore been available. Certain of these covers have been manually movable to open and closed positions and others have been power-operted. While such covers have been generally satisfactory, they have not been entirely satisfactory particularly in respect of the ease and convenience of operation, tight closure of all areas of the truck body opening, and, conversely, full clearance of all areas of the body opening with the cover in its open position.